WHAT IS THE VALUE OF A,B,C,D ?

Question

A+B =8

A+C =13

B+D =8

C-D  =6

WHAT IS THE VALUE OF A,B,C,D ?

 

Answer 1

There are four independent equations with four variables.  That means that we can solve for all four variables (A,B,C,D).

 

We may use either (1) substitution [that is, solve for one variable and plug that into other equations until a value for that variable is found, than plug that into another equation, etc.] or (2) a form of elimination [this resembles what you might someday learn using matrix operations].  Let's do #2:

 

 A   +  B                    =    8          [eq1]

 A   +          C            =  13         [eq2]

          B          +   D   =   8         [eq3]

                  C   -   D   =   6         [eq4]

----------------------------------   {eliminate D by adding four equations]

2A + 2B + 2C            =   35

2A + 2B                    =   16        [2*eq1]

----------------------------------    [eliminate A and B by subtracting equations]

                 2C           =   19

                   C           =   9.5

 

  A   +          C           =  13       [eq2 again]

                   C           =    9.5    

---------------------------------   [eliminate C by subtracting equations]

  A                            =   3.5

 

  A  +  B                    =  8        [eq1 again]

  A                            =  3.5

--------------------------------    [eliminate A by subtracting equations]

          B                    =  4.5

 

          B  +         D    =  8        [eq3 again]

          B                    =  4.5

 ------------------------------     [eliminate B by subtracting equaitons]

                         D    =   3.5

 

Check:

A + B = 8       3.5 + 4.5 = 8 ?    8=8  ?yes

A + C = 13     3.5 + 9.5 = 13  ?   13 = 13  ?yes

B + D = 8       4.5 + 3.5 = 8  ?    8 = 8  ?yes

C - D = 6        9.5 - 3.5 = 6  ?   6 = 6  ?yes